Question

You are a student in a science class that is using the following
apparatus to determine the value of g. Two photogates are used.
(Note: You may be familiar with photogates in everyday living. You
see them in the doorways of some stores. They are designed to ring
a bell when someone interrupts the beam while walking through the
door.) One photogate is located at the edge of a 1.00-m-high table
and the second photogate is located on the floor directly below the
first photogate. You are told to drop a marble through these gates,
releasing it from rest at the same height as the table. The upper
gate starts a timer as the ball passes through it. The second
photogate stops the timer when the ball passes through its
beam.
(a) Prove that the experimental magnitude of free-fall acceleration
is given by gexp = (2(Delta)y)/(delta)t)^2, where (delta)y is the
vertical distance between the photogates and ?t is the fall time.
(Do this on paper. Your instructor may ask you to turn in this
work.)

(b) For your setup, what value of (delta symbol)t would you expect
to measure, assuming gexp is the standard value (9.81 m/s2)?
(Answer in seconds)

(c) During the experiment, a slight error is made. Instead of
locating the first photogate even with the top of the table, your
not-so-careful lab partner locates it 0.50 cm lower than the top of
the table. However, she does manage to properly locate the second
photogate on the floor directly below the first. What value of gexp
will you and your partner determine? (Answer in m/s^2)

What percentage difference does this represent from the standard
value of g?